United travel to Spain for the first leg of their Champions League last-16 tie, with most of the headlines revolving around Cristiano Ronaldo facing his old club for the first time since leaving in 2009.
Carrick believes that while stopping Ronaldo will be crucial, he must play his part by dictating a midfield battle full of international stars.
He told Sky Sports News: "The headlines will all focus on Cristiano but Real Madrid have real strength in depth.
"We respect the players and history of the club but we are approaching both legs with a squad full of confidence. From a personal point of view, you always want to play against the best teams in the best stadiums and Real Madrid and the Bernabeu certainly fall into that bracket."
The 31-year-old won the Champions League with United in 2008 and has made it to the final on two more occasions.